There’s a feeling you get, sort of like a low-grade fever, when a film franchise is starting to run down. It’s had three or four sequels, it’s going through the motions, there’s no more fresh terrain left to plow. That sensation hovers, like a gray cloud, over “The Girl in the Spider’s Web,” a movie that takes the feminist-hellion mystique of the haunted goth hacker Lisbeth Salander and combines it with a plot — about stopping a computer file with nuclear codes from falling into the wrong hands — that might have come out of a “Die Hard” chapter from the early ’90s. Is it any wonder that the movie is watchable, but that the thrill is gone?

The strange thing is, it’s only the second entry in the Hollywood version of the “Dragon Tattoo” series. So there’s no reason for it to feel this worn out. There were, of course, the three Swedish films, based on the thriller novels that Stig Larsson left when he died (he had planned to write 10). But very few moviegoers in the U.S. saw those. A lot of critics love them, but the films have more diligence than they do style or mood. Theoretically, the American version of this franchise should have been a major blockbuster.

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From the start, though, there’s been a certain lackadaisical who cares? vibe attached to it. The anticipation that surrounded David Fincher’s darkly sleek and gleaming 2011 adaptation of “The Girl with the Dragon Tattoo” built and built and built…until the film actually came out, at which point just enough people went to see it to squeak it past the $100 million finish line. Yet it didn’t really seem like anyone cared all that much. Personally, I thought the picture was terrific: dread-ridden and incendiary, and Rooney Mara, clattering away at the keyboard in fingerless gloves, held down the center of it like a sadomasochistic wraith. I honestly expected “The Girl with the Dragon Tattoo” to be a sensation, but Lisbeth, it turns out, didn’t catch fire in the culture any more than she already had. It felt as if the character had already been digested and absorbed. Maybe that’s why Fincher backed out of the sequel.

In “The Girl in the Spider’s Web,” based on the fourth “Millennium” novel (the first one to be penned — by David Lagercrantz — after Larsson’s death, in order to keep the fans happy and the cash cow flowing), the gifted Claire Foy, with those oversize sensitive marble eyes, takes over the role, but if anything she comes off as more dutiful, less ominously game-on than Rooney Mara. The movie is framed by Lisbeth’s primal family trauma — the rift with her sister that hangs around her like a chain and turns their power-game relationship into a perverse, dysfunctional, abusive-daddy version of the one in “Frozen.” But for most of the film, Lisbeth might be a generic international agent with a nose ring. Foy tries to inject her with a woeful gravity, but the film loses the pulse of what made her a revolutionary character.

And here’s the rich irony of that failure. We are now in the perfect moment to rediscover the meaning of Lisbeth’s mission — her compulsion to cleanse the world of toxic male power and violence. That crusade is, of course, the grand theme of Larsson’s novels. And though the ho-hum response to the Fincher/Mara version of “The Girl with the Dragon Tattoo” indicated that the times had already taken the edge off that theme, the reckoning — the furious sexual-political earthquake — launched a year ago by the Harvey Weinstein scandal should have been the ultimate shot in the arm for this series.

It still could be. For that to happen, though, the series will have to reconnect with what made Lisbeth such a great, scary, brave, inflammatory heroine, and it will have to do so in ways that are willing to shock and unnerve us. The next film, if there is one, needs to be less thriller-logistical and more scaldingly personal. And the best way to accomplish that, frankly, would be for the producers to start from scratch. Throw out the David Lagercrantz novels; they’re not necessary. Instead, craft a story that plugs Lisbeth into the intimate secrets — corporate, erotic, domestic — of how life is being lived today. Make an up-to-the-minute movie with a touch of scandal. Make a thriller that dares to be relevant. Because the trouble with “The Girl in the Spider’s Web” isn’t that it’s badly made, but that it gives you the depressive franchise feeling that it’s a movie connected to nothing but itself. The girl with the dragon tattoo shouldn’t become the girl who turns revenge into a glum gig.

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